Accelerated Multipole Algorithms and Implementations (Rankin, Humphres, Board) Work continued this year importing new algorithmic variants developed in various test programs into out supported "D-PMTA" (Distributed Parallel Multipole Tree Algorithm) code. Many of these variants were developed in serial codes, and so parallelizing them is part of the porting process. Specifically, the macroscopic finite periodic boundary code, the Lennard-Jones potential code, and the more efficient multipole formulation reported last year were all incorporated into D-PMTA this year. Work continues on optimizing D-PMTA for both low speed (networks of workstations with PVM and ethernet/FDDI/ATM) and higher speed (Cray T3D/T3E) distributed machines. Particular success in hiding the latency of messages in the low speed environment has been achieved and is reported in one of the papers listed below (Rankin and Board). Variable Box Size and Shape (Rankin, Humphres, Board) Working with Dr. Jan Hermans at UNC-Chapel Hill, we developed a multipole formulation suited to the needs of constant-pressure MD calculations, where the simulation box size needs to adjust dynamically (and isotropically). This work is being extended to handle non-cubic simulation cells which can also maintain constant pressure. Publication of the isotropic case is expected in early '97; the non-cubic case is a new project. Parallel Ewald methods (Toukmaji, Board) We have worked with Dr. Tom Darden at NIEHS to develop a parallel variant of Darden's Particle-Mesh Ewald code, a fast method for performing Ewald summation when infinite periodic boundary conditions are in use. A parallel version for cubic unit cells is now available, with a version for arbitrary parallelepipeds to follow soon. This fast Ewald code competes favorably for computation time with our multipole code enhanced with macroscopic but finite periodic boundary conditions on small numbers of processors but does not scale well yet to large numbers of processors. Both methods remain promising for large scale periodic simulations. A publication has been accepted on this work and will be out this fall. Macroscopic Methods (Lambert, Board) The method for incorporating finite but macroscopically large periodic boundary conditions in the multipole algorithm framework first reported in last year's report has been further refined, so that the cost for simulating, say, the effect of a cubic meter of water on the central simulation cell of perhaps 100,000 atoms is only 10-20% more than a simulation of the central simulation cell alone. Work continued this year on parallelizing the method, which was reported in serial form last year. A journal article on this work has been accepted. Fast Algorithm for Hessian Matrix-Vector Product (Lambert) We reported last year an unexpected application of multipole techniques in the problem of forming matrix-vector products, a major bottleneck in Prof. Schlick's long-timestep methods. Lambert spent a month at NYU working with Schlick's group to develop these ideas; they form the basis of his dissertation proposal and are under active investigation. Details of the method have been worked out and an implementation is in progress. New Algorithmic Initiatives (Board, Toukmaji, Majercik) Working with Dr. Darden, we are developing methods to incorporate polarization effects into our multipole framework. The inclusion of polarizable particles in the multipole calculations is not fundamentally difficult, as it is straightforward to compute the multipole expansion of a group of dipoles, but the memory requirements and bookkeeping are non-trivial. Incorporation of polarizable particles into Ewald codes is also being explored. First publication of this work is expected in early '97. Working with Dr. Hermans, we are investigating the complexity of incorporating free energy calculations into the multipole framework. Use of the particle insertion method for free energy calculations results in particles which are morphed in and out of existence; this causes some complications in recomputing the multipole moments of groups of particles but we do not expect these to be difficult to manage. This work is just beginning. As stated above: in the work planned for next year, our main initiatives are in polarization, free energy, non-cubic boxes, and ongoing work to improve the speed and flexibility of both the Ewald and multipole codes.